Private Page visible via URL and not search box

I’d like to supply a client with a private page, accessible only via a URL and not indexed so it doesn’t appear on the Google SERP.

I’ve set the page to NOINDEX, NOFOLLOW but the page can still be found using the Insite Search Box.
I’ve tried setting the page to Private but then it’s only visible to people logged into the website.
The only other option I can see is setting a password, but then I have the hassle of ensuring everyone who needs access has the password (and shares it with other colleagues).

Is there a way of having a page that is accessed using a URL but can’t be found by any other means?

All advice gratefully received.
Jamie